NEET
Practice Test 9
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Moment of inertia of a circular wire of mass M and radius R about its diameter is

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected ?

  • Solution

    Angular momentum will remain the same since external torque is zero

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB Such that

where dA and dB are their densities.

  • Solution

    \(\frac{I_{A}}{I_{B}}=\frac{d_{A}}{d_{B}}\)

    ∴IA< IB

The angular momentum of a system of particle is conserved

  • Solution

    We know that \(\tau _{ext}=\frac{dL}{dt}\)

    if angular momentum is conserved, it means change in angular momentum = 0

    or,dL=0,\(\frac{dL}{dt}=0\Rightarrow \tau _{ext}=0\)

A hollow sphere is held suspended. Sand is now poured into it in stages.

The centre of gravity of the sphere with the sand

  • Solution

    Initially centre of gravity is at the centre. When sand is poured it will fall and again after a limit, centre of gravity will rise.

Moment of inertia does not depend upon

  • Solution

    Basic equation of moment of inertia is given

    \(I=\sum_{i-1}^{n}m_{i}r_{i}^{2}\)

    where mi is the mass of ith particle at a distance of ri from axis of rotation.Thus it does not depend on angular velocity

Analogue of mass in rotational motion is

  • Solution

    Analogue of mass in rotational motion is moment of inertia. It plays the same role as mass plays in translational motion

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement 1 :A wheel moving down a frictionless inclined plane will slip and not roll on the plane.

Statement 2 :It is the frictional force which provides a torque necessary for a body to roll on a surface.

  • Solution

    (b) Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement 1 :If no external force acts on a system of particles, then the centre of mass will not move in any direction.

Statement 2 :If net external force is zero, then the linear momentum of the system remains constant.

  • Solution

    (a)Statement -1 is false, Statement-2 is true

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement 1:A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity.Then the acceleration of lowest point on the disc is zero.

Statement 2 :For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero.

  • Solution

    (a)Statement -1 is false, Statement-2 is true

    For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of lowest point of disc is directed vertically upwards and is not zero (Due to translation part of rolling,acceleration of lowest point is zero. Due to rotational part of rolling, the tangential acceleration of lowest point is zero and centripetal acceleration is non-zero and upwards). Hence statement 1 is false.

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SYSTEM OF PARTICLES AND ROTATIONAL MOTION
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